FOXBOROUGH — This one was right up there with the Bruins’ win against the Maple Leafs in Game 7 and David Ortiz’s season-changing grand slam against the Tigers. The Patriots should have imported Boston cop Steve Horgan to signal “good” when Stephen Gostkowski split the uprights early Monday morning.

On one of the coldest nights in Gillette Stadium history, the Patriots trailed Denver, 24-0, at halftime, then rallied to beat the Broncos, 34-31, in overtime. Gostkowski’s 31-yard field goal with less than two minutes left in overtime won it just before 12:30 a.m.

“Really proud of the way they played, the way they hung in there,’’ said Patriots coach Bill Belichick. “We just stuck it out and made plays.’’

More than that, the Patriots did what they always seem to do: They waited for the other guys to beat themselves. After almost 75 minutes of freezing football, the big break came when the Patriots punted the ball and Denver’s Tony Carter ran under the ball. While Broncos return man Wes Welker frantically tried to keep everyone away from the kick, the ball dropped on clueless Carter, New England’s Nate Ebner recovered, and the Patriots took over at the Denver 13-yard line. From there, it was just a matter of lining up for the winning kick.

This is the true, time-tested Patriot Way. Wait for the other guy to wet his pants. It works every time. It doesn’t matter if it’s Sean Payton or Peyton Manning. Sooner or later, the other guys step on their own feet.

We spent all week talking about Tom Brady vs. Manning, and the return of Welker. But the big theme on a frigid night (6 degree windchill) was ball security. This was a game with 11 fumbles. Manning completed 19 of 36 for 150 yards. Brady was 34 of 50 for 344 yards. Denver’s Knowshon Moreno ran for 224 yards.

The frozen faithful who stayed were rewarded. In the last 50 years of NFL play, only six teams have recovered from a 24-point halftime deficit. Six out of nearly 500. This is not something you see every day.

The Patriots were awful in the first half. They lost fumbles on their first three possessions. They fumbled six times in the first 20 minutes. They fell behind, 24-0, at halftime and a few fans went home.

The frozen faithful who stayed were rewarded. In the last 50 years of NFL play, only six teams have recovered from a 24-point halftime deficit. Six out of nearly 500. This is not something you see every day.

“We didn’t give ourselves a chance in the first half,’’ said Brady. “It was a terrible half of football. Our defense really bailed us out.’’

With 2:57 left in the first quarter, the Patriots had three fumbles in three possessions and the Broncos led, 17-0, even though Manning had only two completions for 8 yards. So much for a week of pregame dissection and analysis.

The Patriots were rolling on their first series when Stevan Ridley had the ball punched out of his right hand by Broncos linebacker Wesley Woodyard. Von Miller scooped up the pigskin and rumbled 60 yards, across the goal line, to make it 7-0. It was the Riddler’s third fumble in three games. We did not see him again.

Seconds later, Brady dropped back to pass from his 28 and was rocked from behind by Miller. The ball came loose, and this time it was gathered by tackle Terrance Knighton, who lumbered to the 10-yard line. Two plays later, Moreno ran it in from the 2 and it was 14-0 with 8:58 left in the first quarter.

In the words of Belichick, that’s not what we were looking for.

It got worse. LeGarrette Blount fumbled on the Patriots’ third possession. Denver settled for a field goal.

A Manning touchdown pass to Jacob Tamme made it 24-0 before halftime. Frozen fans booed the Patriots off the field at intermission.

Surprisingly, a good number of fans returned after halftime and were rewarded with 31 straight points by the home team. It started with a touchdown pass to Julian Edelman. After a Denver fumble, the Patriots scored again on a Brandon Bolden 1-yard run. With 19 seconds left in the third, Brady connected with Rob Gronkowski on a 6-yard touchdown dart to cut it to 24-21.

The surge continued. Manning fumbled. Then Manning was intercepted and the Patriots converted, taking a 28-24 lead on a 14-yard touchdown pass from Brady to Julian Edelman. A subsequent Patriots field goal made it 31-24. It felt like it was just a matter of time. This game was too big for Broncos interim coach Jack Del Rio. It looked like the Patriots were going to be the first team in NFL history to win in a blowout after trailing, 24-0, at halftime.

Then Manning pushed back. He drove the Broncos 80 yards in 10 plays, capping the drive with an 11-yard touchdown pass to Demaryius Thomas.

The Patriots won the coin flip in overtime (do they ever lose a coin flip?) and Belichick chose the wind over the ball. He let the Broncos have the first possession.

It worked. Both teams had the ball twice and failed to score. Then the Patriots punted it away one last time and waited for their break. Carter, an ex-Patriot (embedded, perhaps), ran under the ball and the rest is history.

Everything is in place. The Patriots are 8-3. They are going to win the AFC East and get a first-round bye and a second-round home game. They are probably going to see the Broncos again, maybe for the AFC championship.